Nontrivial topology and the chiral Schwinger model.

Abstract

We analyze the chiral Schwinger model in nontrivial topological sectors, performing its complete bosonization. In order to do this, we propose a prescription for evaluating the fermion determinant in the presence of the zero modes, valid for non-Hermitian Dirac operators, in general. By taking fermionic external sources into account in every step of the calculation, we discover a phase ambiguity which affects the effective action and can be used to render the result invariant with respect to particular choices of the topologically charged background configuration. Consistency requirements on the bosonization procedure fix the phase ambiguity and determine a unique value for the Jackiw-Rajaraman regularization parameter in all sectors with a nonzero topological charge. We thus find that nontrivial sectors have a null contribution to all fermionic correlation functions. Our method is also checked against the analogous results for the Schwinger model.